How do you find the slope perpendicular to (-7,2) and (5,-12)?

Question

Hazel Anglin · Accepted Answer

#m_("perpendicular")=6/7# #"given a line with slope m then the slope of a line"# #"perpendicular to it is "# #•color(white)(x)m_(color(red)"perpendicular")=-1/m# #"to calculate m use the "color(blue)"gradient formula"# #•color(white)(x)m=(y_2-y_1)/(x_2-x_1)# #"let "(x_1,y_1)=(-7,2)" and "(x_2,y_2)=(5,-12)# #rArrm=(-12-2)/(5-(-7))=(-14)/(12)=-7/6# #rArrm_(color(red)"perpendicular")=-1/(-7/6)=6/7#

Eva Abramson · Answer

undefined To find the slope perpendicular to a given line, first calculate the slope of the given line using the formula:

$$ m = \frac{{y2 - y1}}{{x2 - x1}} $$

Then, determine the negative reciprocal of this slope to find the slope perpendicular to the given line. So, if the slope of the given line is $ m $, the slope perpendicular to it is $ -\frac{1}{m} $.

Using the coordinates (-7,2) and (5,-12), the slope of the given line is:

$$ m = \frac{{-12 - 2}}{{5 - (-7)}} = \frac{{-14}}{{12}} = -\frac{7}{6} $$

The slope perpendicular to this line is the negative reciprocal of $ -\frac{7}{6} $, which is:

$$ -\frac{1}{{-\frac{7}{6}}} = \frac{6}{7} $$

So, the slope perpendicular to the line passing through (-7,2) and (5,-12) is $ \frac{6}{7} $.